Revista Matemática Iberoamericana


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Volume 22, Issue 1, 2006, pp. 55–92
DOI: 10.4171/RMI/449

Published online: 2006-04-30

Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one

Alexander V. Sobolev[1]

(1) University College London, UK

We consider a periodic pseudo-differential operator on the real line, which is a lower-order perturbation of an elliptic operator with a homogeneous symbol and constant coefficients. It is proved that the density of states of such an operator admits a complete asymptotic expansion at large energies. A few first terms of this expansion are found in a closed form.

Keywords: Periodic pseudodifferential operators, density of states

Sobolev Alexander: Asymptotics of the integrated density of states for periodic elliptic pseudo-differential operators in dimension one. Rev. Mat. Iberoam. 22 (2006), 55-92. doi: 10.4171/RMI/449